Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating propagation velocity terms are discretized using central
differences, stability problems occur when the grid spacing is chosen
too coarse. In this paper, we introduce the splitting modified donorcell
scheme for avoiding stability problems and prove that it is
consistent to the modified donor-cell scheme with same accuracy. The
splitting modified donor-cell scheme was adopted to split the wave
spectral action balance equation into four one-dimensional problems,
which for each small problem obtains the independently tridiagonal
linear systems. For each smaller system can be solved by direct or
iterative methods at the same time which is very fast when performed
by a multi-cores computer.